| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Function Transformations |
| Type | Modulus function transformations |
| Difficulty | Standard +0.3 This is a standard C3 transformations question involving logarithms. Parts (i)-(iii) require routine application of transformation rules (translation, stretch, and reflection in x-axis for modulus). Part (iv) tests understanding that |f(x)| = -f(x) when f(x) ≤ 0, requiring students to solve ln(½x - a) ≤ 0. While multi-part, each component uses familiar techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.02l Modulus function: notation, relations, equations and inequalities1.02w Graph transformations: simple transformations of f(x)1.02x Combinations of transformations: multiple transformations |
The curve $y = \ln x$ is transformed to the curve $y = \ln(\frac{1}{2}x - a)$ by means of a translation followed by a stretch. It is given that $a$ is a positive constant.
\begin{enumerate}[label=(\roman*)]
\item Give full details of the translation and stretch involved. [2]
\item Sketch the graph of $y = \ln(\frac{1}{2}x - a)$. [2]
\item Sketch, on another diagram, the graph of $y = |\ln(\frac{1}{2}x - a)|$. [2]
\item State, in terms of $a$, the set of values of $x$ for which $|\ln(\frac{1}{2}x - a)| = -\ln(\frac{1}{2}x - a)$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR C3 Q7 [8]}}